So far, several methods have been found to determine the stable
homotopy groups of spheres. For example we have the classical Adams
spectral sequence (ASS) (cf. [1]}) based on the
Eilenberg-MacLane spectrum \(K\mathbb {Z}_p\) , whose \(E_2\) -term is
\({\rm Ext}_A^{s, t}(\mathbb {Z}_p, \mathbb {Z}_p)\) 
and the Adams differential is given by \( d_r: E_r^{s, t}\rightarrow E_r^{s+r, t+r-1}\) .
We also have the Adams-Novikov spectral sequence
based on the Brown-Peterson spectrum
\(BP\) (cf. [2]}, [3]}, [4]}).
